A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+
t2)is obtained,which is verified by the numerical results.

The thermal effect in diode-end-pumped continuous-wave 914-nm Nd:YVO_4 laser

The thermal effect and the heat generation in diode-end-pumped continuous-wave 914-nm Nd：YVO4 lasers are investigated in detail. A theoretical model of a diode end-pumped solid-state laser is constructed to analyse the influence of fractional thermal loading on the thermal effect in the Nd：YVO4 laser based on finite element analysis. The thermal focal lengths and the end-surface deformations of laser rods in Nd：YVO4 quasi-three-level and four-level lasers are measured and compared with the results obtained by ordinary interferometry for the demonstration of higher thermal loading in 914-nm laser. Finally the fractional thermal loading in the Nd：YVO4 quasi-three-level laser is calculated by matching the experimental and the simulated end deformations.

ANALYSIS OF BRANCHING DISTRIBUTION IN POLYETHYLENES BY DIFFERENTIAL SCANNING CALORIMETRY

Short chain branching has been characterized using thermal fractionation, a stepwise isothermal crystallizationtechnique, followed by a melting analysis scan using differential scanning calorimetry. Short chain branching distributionwas also characterized by a continuous slow cooling crystallization, followed by a melting analysis scan. Four differentpolyethylenes were studied: Ziegler-Natta gas phase, Ziegler-Natta solution, metallocene, constrained-geometry single sitecatalyzed polyethylenes. The branching distribution was calculated from a calibration of branch content with meltingtemperature. The lamellar thickness was calculated based on the thermodynamic melting temperature of each polyethyleneand the surface free energy of the crystal face. The branching distribution and lamellar thickness distribution were used tocalculate weight average branch content, mean lamellar thickness, and a branch dispersity index. The results for the branchcontent were in good agreement with the known comonomer content of the polyethylenes. A limitation was that high branchcontent polyethylenes did not reach their potential crystallization at ambient temperatures. Cooling to sub-ambient wasnecessary to equilibrate the crystallization, but melting temperature versus branch content was not applicable after cooling tobelow ambient because the calibration data were not performed in this way.

Time fractional dual-phase-lag heat conduction equation

We build a fractional dual-phase-lag model and the corresponding bioheat transfer equation, which we use to interpret the experiment results for processed meat that have been explained by applying the hyperbolic conduction. Analytical solutions expressed by H-functions are obtained by using the Laplace and Fourier transforms method. The inverse fractional dual-phase-lag heat conduction problem for the simultaneous estimation of two relaxation times and orders of fractionality is solved by applying the nonlinear least-square method. The estimated model parameters are given. Finally, the measured and the calculated temperatures versus time are compared and discussed. Some numerical examples are also given and discussed.

Fractional thermoelasticity applications for porous asphaltic materials

A new mathematical model of poro-thermoelasticity has been constructed in the context of a new consideration of heat conduction with fractional order.One-dimensional application for a poroelastic half-space saturated with fluid is considered.The surface of the halfspace is assumed to be traction-free,permeable,and subjected to heating.The Laplace transform technique is used to solve the problem.The inversion of the Laplace transform will be obtained numerically and the numerical values of the temperature,stresses,strains,and displacements will be illustrated graphically for the solid and the liquid.

Fractionation of Polyolefin Elastomer by a Modified SSA Technique

As an important part of semicrystalline polymer materials,polyolefin elastomers are widely used,and the in-depth analysis of their molecular chain structure information is of great significance to promote their rapid development.We show in this work an effort in characterizing a commercial polyolefin elastomer of ethylene/1-octene copolymer by a modified successive self-nucleation and annealing(SSA)technique.A small amount of linear polyethylene was blended with the ethylene/1-octene copolymer serving as nucleation agent during SSA.It turned out that a tiny fraction of linear polyethylene can significantly promote the crystallization of the copolymer during cooling from different annealing temperatures and increase the melting temperature of the fractions so that providing apparent methylene sequence length much closer to the real value than obtained by traditional SSA technique.

Phosphate removal from domestic wastewater using thermally modified steel slag

This study was performed to investigate the removal of phosphate from domestic wastewater using a modified steel slag as the adsorbent. The adsorption effects of alkalinity, salt, water,and thermal modification were investigated. The results showed that thermal activation at 800℃ for 1 hr was the optimum operation to improve the adsorption capacity. The adsorption process of the thermally modified slag was well described by the Elovich kinetic model and the Langmuir isotherm model. The maximum adsorption capacity calculated from the Langmuir model reached 13.62 mg/g. Scanning electron microscopy indicated that the surface of the modified slag was cracked and that the texture became loose after heating. The surface area and pore volume did not change after thermal modification. In the treatment of domestic wastewater, the modified slag bed（35.5 kg） removed phosphate effectively and operated for 158 days until the effluent P rose above the limit concentration of 0.5 mg/L. The phosphate fractionation method, which is often applied in soil research, was used to analyze the phosphate adsorption behavior in the slag bed. The analysis revealed that the total contents of various Ca-P forms accounted for 81.4%-91.1%, i.e., Ca10-P 50.6%-65.1%, Ca8-P 17.8%-25.0%,and Ca2-P 4.66%-9.20%. The forms of Al-P, Fe-P, and O-P accounted for only 8.9%-18.6%. The formation of Ca10-P precipitates was considered to be the main mechanism of phosphate removal in the thermally modified slag bed.